A Robust Higher-Order Scheme for Fractional Delay Differential Equations Involving Caputo Derivative

Abstract

This article considers nonlinear fractional delay differential equations involving Caputo’s fractional derivative of order \(\alpha \in (0,1)\). We focus on designing a robust numerical algorithm of order \(O(h^{4-\alpha })\). To achieve this, we developed a higher-order interpolation-based approximation for Caputo’s derivative, which enables us to construct a robust numerical scheme for the considered problem. Furthermore, we discuss the stability and error analysis of the proposed higher-order scheme. Finally, numerous examples, including real-life applications, are evaluated to demonstrate the computational efficiency of the proposed algorithm.